Overview

This text is a comprehensive study of the theory of continuous selections of multivalued mappings. This branch of modern topology was introduced by E.A. Michael in the 1950s and has since witnessed an intensive development with various applications outside topology, e.g. in geometry of Banach spaces, manifolds theory, convex sets, fixed points theory, differential inclusions, optimal control, approximation theory, and mathematical economics. The work can be used in different ways: the first part is an exposition of the basic theory, with details. The second part is a comprehensive survey of the main results. Lastly, the third part collects various kinds of applications of the theory.

Full Product Details

Author:   D. Repovs ,  P.V. Semenov
Publisher:   Springer
Imprint:   Springer
Edition:   1998 ed.
Volume:   455
Dimensions:   Width: 15.50cm , Height: 2.20cm , Length: 23.50cm
Weight:   1.540kg
ISBN:  

9780792352778

ISBN 10:   0792352777
Pages:   359
Publication Date:   30 September 1998
Audience:   College/higher education ,  Professional and scholarly ,  Undergraduate ,  Postgraduate, Research & Scholarly
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

A. Theory.- §0. Preliminaries.- §1. Convex-valued selection theorem.- §2. Zero-dimensional selection theorem.- §3. Relations between Zero-dimensional and Convex-valued selection theorems.- §4. Compact-valued selection theorem.- §5. Finite-dimensional selection theorem.- §6. Examples and counterexamples.- §7. Addendum: New proof of Finite-dimensional selection theorem.- B. Results.- §1. Characterization of normality-type properties.- §2. Unified selection theorems.- §3. Selection theorems for non-lower semicontinuous mappings.- §4. Selection theorems for nonconvex-valued maps.- §5. Miscellaneous results.- §6. Measurable selections.- C. Applications.- §1. First applications.- §2. Regular mappings and locally trivial fibrations.- §3. Fixed-point theorems.- §4. Homeomorphism Group Problem.- §5. Soft mappings.- §6. Metric projections.- §7. Differential inclusions.- References.

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